Monte Carlo testing of the statistical analysis of nucleation data

A method is proposed for experimentally determining the magnitude of the preexponential and exponential factors in the nucleation rate equation. The method is a modification of a statistical approach developed by Skripov, which allows nucleation data, such as a collection of undercoolings prior to nucleation, to be analyzed to yield quantitative information on the nucleation rate equation. Three expressions for the nucleation rate equation (Fisher-Turnbull Spaepen-Turnbull, and Thompson-Spaepen) were used to generate probability distributions of nucleation events as a function of temperature. The probability density functions generated from these expressions differ for the homogeneous nucleation case when normalized to a common mode undercooling. However, for common mode undercoolings in the heterogeneous regime (approximately 15% T-m undercooling) the resulting probability distributions are quite similar. To test the approach and evaluate the uncertainty of the statistical analysis, nucleation data sets were simulated by a Monte Carlo technique. For data sets of 100 experimental runs, the uncertainty in the exponential factor and the log of the preexponential factor is 10% if temperature measurement is exact. The implications of temperature measurement uncertainty were evaluated numerically. (C) 1998 Acta Metallurgica Inc.